Exact solution for the interior of a black hole

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1、FluctuationandNoiseLettersVol.0,No.0(2008)000–000cWorldScientificPublishingCompanyEXACTSOLUTIONFORTHEINTERIOROFABLACKHOLETHEOM.NIEUWENHUIZENInstituteforTheoreticalPhysics,UniversityofAmsterdamValckenierstraat65,1018XEAmsterdam,TheNetherlandsReceived(receiveddate

2、)Revised(reviseddate)Accepted(accepteddate)WithintheRelativisticTheoryofGravitationitisshownthattheequationofstatep=ρholdsnearthecenterofablackhole.Forthestiffequationofstatep=ρ−ρctheinteriormetricissolvedexactly.ItismatchedwiththeSchwarzschildmetric,whichisdefo

3、rmedinanarrowrangebeyondthehorizon.Thesolutionisregulareverywhere,withaspecificshapeattheorigin.Thegravitationalredshiftatthehorizonremainsfinitebutislarge,z∼1023M⊙/M.Timekeepsitsstandardrolealsointheinterior.TheenergyoftheSchwarzschildmetric,showntobeminusinfinit

4、yintheGeneralTheoryofRelativity,isregularizedinthissetup,resultinginE=Mc2.Keywords:Blackholeinterior,stiffequationofstate,vacuumequationofstate,Rela-tivisticTheoryofGravitation,bimetrictheory,exactsolutionarXiv:0805.4169v1[gr-qc]27May20081.IntroductionBlackholes

5、(BH’s)havefascinatedmankindbecauseoftheirpredictedproperties:attheclassicallevelnotevenlightcanescape;themassislocatedinthecenter;theroleoftimeintheinteriorisplayedbyspaceandviceversa;onthequantumleveltheyradiateasathermalbodyviatheHawkingmechanism.Thestructure

6、ofgalaxiesisrelatedtoastrophysicalBH’s,galaxiesarebelievedtohaveasupermassivecentralblackholewithmassequalto0.12%ofthebulgemass.[1]TheBHinthecenterofourownGalaxyhas“only”fourmillionsolarmasses.SomebelievethatourUniverseisactuallytheinsideofagiantblackhole.[2]As

7、theabovementionedtheoreticalaspectsarephysicallydifficulttounderstand,animportantquestionis:Aretheyperhapsunrealistic,andshouldthebehaviorofphysicalBH’snotbesoughtinamodifiedversionoftheGeneralTheoryofRelativity(GTR)?OnesuchcandidateistheRelativisticTheoryofGravit

8、ation(RTG)proposedbyLogunov.[3,4]Followingidea’sofRosen[5]andothers,e.g.[6,7],itwritestheHilbert-EinsteinLagrangianintermsofafieldinMinkowskispace-time,extendsitwiththecosmol